Problem: Subtract the following rational expressions. $\dfrac{4-6k^3}{3+k^3}-\dfrac{-2k^2+7}{3+k^3}=$
Solution: We want to subtract two rational expressions whose denominators are equal. We can do this by subtracting the numerators and keeping the denominator the same. [Does this fit with how we subtract rational numbers?] $\begin{aligned} &\phantom{=}\dfrac{4-6k^3}{3+k^3}-\dfrac{-2k^2+7}{3+k^3} \\\\ &=\dfrac{(4-6k^3)-(-2k^2+7)}{3+k^3} \\\\ &=\dfrac{4-6k^3+2k^2-7}{3+k^3} \\\\ &=\dfrac{-6k^3+2k^2-3}{3+k^3} \end{aligned}$ In conclusion, $\dfrac{4-6k^3}{3+k^3}-\dfrac{-2k^2+7}{3+k^3}=\dfrac{-6k^3+2k^2-3}{3+k^3}$